question_answer

Distance of the centre of mass of a solid uniform cone from its vertex is \[{{z}_{0}}\]. If the radius of its base is R and its height is h then \[{{z}_{0}}\] is equal to

A) \[\frac{{{h}^{2}}}{4R}\]        

B) \[\frac{3{{h}^{{}}}}{4}\]

C) \[\frac{5{{h}^{{}}}}{8}\]                  

D) \[\frac{3{{h}^{2}}}{8R}\]

Correct Answer: B

Solution :

[b] \[dm=\pi {{r}^{2}}.dy.r\] \[{{y}_{CM}}=\frac{\int{ydm}}{\int{dm}}=\frac{\int_{0}^{h}{\pi {{r}^{2}}dy\times \rho \times y}}{\frac{1}{3}\pi {{R}^{2}}h\rho }=\frac{3h}{4}\]